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Golden Cookie Probabilities
This page lists the actual probabilities over the long term for getting each Golden/Wrath cookie effect. For detailed information on the effects of Golden Cookies and Wrath Cookies, see their respective pages. Further calculations can be found in Expected Long Term Cookie Production. Version 2 The process for choosing a cookie effect is as follows: First, the cookie is either a Golden cookie or a Wrath cookie. The probability for a Wrath cookie is either 0, 1/3, 2/3, or 1, depending on the Grandmapocalypse stage. Then, possible effects are added to a list, and finally, a random effect from the list is chosen. For Golden cookies, this process is as follows: * Add Frenzy and Lucky to a list. * 3% chance to add Chain to the list, if at least 100000 cookies have been baked this game. * 10% chance to add Click Frenzy to the list. * 15% chance to add Dragon Harvest and/or Dragonflight to the list, if their auras are set. * 80% chance to remove the last effect from the list, if it's there. * 0.01% chance to add Blab to the list. * Pick a random effect from the list. And for Wrath cookies: * Add Clot, Lucky, and Ruin to a list * 30% chance to add Elder Frenzy and Chain to the list. * If previous step fails (70%), 3% chance to add Chain to the list, if at least 100000 cookies have been baked this game. * 10% chance to add Click Frenzy to the list. * 5% chance to add Dragon Harvest and/or Dragonflight to the list, if their auras are set. * 80% chance to remove the last effect from the list, if it's there. * 0.01% chance to add Blab to the list. * Pick a random effect from the list. All calculations will assume that at least 100000 cookies have been baked. Appeased If neither dragon aura is set, this process is identical to version 1.0466, so the probabilities are: Using the same process as in the previous calculations (below), the rest of the probabilities are as follows. With Dragon Harvest or Dragonflight: With both: Awoken With neither dragon aura: With Dragon Harvest or Dragonflight: With both: Displeased With neither dragon aura: With Dragon Harvest or Dragonflight: With both: Angered With neither dragon aura: With Dragon Harvest or Dragonflight: With both: Version 1.0466 Appeased As of version 1.0466, this is how the game picks a golden cookie effect: * Add Frenzy and Lucky to a list. * 3% chance to add Chain to the list. * 10% chance to add Click Frenzy to the list. * 80% chance to remove the last effect from the list, if it's there. * 0.01% chance to add Blab to the list. * Pick a random effect from the list. From this process, we can build the following table of probabilities for which items will be in the list: If the last cookie is Frenzy or Lucky, then there is a 20% chance of the numbers in the table above, and an 80% chance of the same probabilities with one less item in the list (Frenzy or Lucky). Adding up the relevant probabilities, divided by the number of items in the list, we can generate the following conditional probability table, given the last cookie: Most of the time Frenzy will alternate with Lucky, with about 1 in 6 or 7 cookies breaking this pattern. Using this as a transition matrix, inside of 20 iterations the overall probability stabilizes, with the following numbers confirming the Monte Carlo technique above: Combining this with the average time between cookie spawns, there should be a stacked frenzy on average once every 92 minutes 43 seconds, or 88 minutes 23 seconds with the Golden Goose Egg. Version 1.0465 Empirical With the Lucky day, Serendipity, and Get Lucky upgrades, any effect may occur while a Frenzy or Clot effect from the preceding cookie is still active. The "Plain Chance" listed below is proportion of all cookies that have the listed effect and are not preceded by Frenzy or Clot, while the "Frenzy Chance" and "Clot Chance" are the proportions of all cookies that have the listed effect and are preceded by the respective effect. Without the three aforementioned upgrades, this overlap isn't possible, and only the Total Chance listed below is relevant. Note that while Frenzy will almost always still be active when the next Golden/Wrath cookie appears, there is a chance (about 1% with Golden goose egg and 10% without it) that a Clot will expire before the next cookie appears. The tables below do not account for this. Also note that the Frenzy, Elder Frenzy, and Clot effects are not modified by an existing Frenzy or Clot, but will instead overwrite the existing effect. The probabilities below were obtained using a Monte Carlo simulation of 500,000,000 cookie spawns for each wrath level, using the logic for cookie generation from Cookie Clicker version 1.0465. Appeased Awoken Displeased Angered